Surface Areas and Volumes quiz

The curved surface area of a cone of radius r and slant height l is:

The surface area of a sphere of radius r is:

The total surface area of a solid hemisphere of radius r is:

The volume of a cone is:

The slant height of a cone with radius 6 cm and height 8 cm is:

The volume of a hemisphere of radius r is:

If the radius of a sphere is halved, its volume becomes:

The surface area of a sphere of radius 7 cm is (pi = 22/7):

A cone and a cylinder have the same radius and height. The ratio of their volumes is:

The curved surface area of a hemisphere of radius 7 cm is (pi = 22/7):

Find the curved surface area of a cone with radius 3.5 cm and slant height 10 cm. (Take pi = 22/7.) (2 marks)

Find the volume of a sphere of radius 3 cm in terms of pi. (2 marks)

Find the height of a cone with radius 5 cm and slant height 13 cm. (2 marks)

Find the total surface area of a hemisphere of radius 10 cm. (Take pi = 3.14.) (2 marks)

The surface area of a sphere is 154 sq cm. Find its radius. (Take pi = 22/7.) (2 marks)

Find the ratio of the surface areas of two spheres with radii 2 cm and 3 cm. (2 marks)

Find the volume of a cone with radius 7 cm and height 6 cm. (Take pi = 22/7.) (2 marks)

Why is the volume of a hemisphere half that of a sphere of the same radius? (2 marks)

A sphere and a hemisphere have the same radius. Find the ratio of their total surface areas. (2 marks)

How many litres of water can a hemispherical tank of radius 2.1 m hold? (Take pi = 22/7, 1 cubic m = 1000 litres.) (2 marks)

The volume of a cone is 1570 cubic cm and its height is 15 cm. Find its radius. (Take pi = 3.14.) (3 marks)

A hemispherical bowl of radius 3.5 cm is made of steel 0.5 cm thick. Find the outer curved surface area of the bowl. (Take pi = 22/7.) (3 marks)

A right triangle with sides 6 cm, 8 cm and 10 cm is rotated about the side 8 cm. Find the volume and curved surface area of the cone formed, in terms of pi. (3 marks)

The diameter of the Moon is approximately one-fourth of the diameter of the Earth. Find the ratio of their surface areas and the ratio of their volumes. (3 marks)

A spherical balloon is inflated so that its radius increases from 7 cm to 14 cm. Find the ratio of the surface areas in the two cases and the increase in volume. (Take pi = 22/7.) (3 marks)

Read the passage and answer the questions. An ice cream cone has a radius of 3.5 cm and height 12 cm, topped with a hemisphere of ice cream of the same radius. (i) Find the slant height of the cone. (ii) Find the volume of ice cream in the cone part. (iii) Find the volume of the hemispherical top, and the total volume. (Take pi = 22/7.) (5 marks)

Read the passage and answer the questions. A joker's cap is in the shape of a right circular cone of base radius 7 cm and height 24 cm. A shop makes 10 such caps. (i) Find the slant height of the cap. (ii) Find the area of sheet needed for one cap. (iii) Find the sheet needed for 10 caps. (Take pi = 22/7.) (5 marks)

Read the passage and answer the questions. A heap of wheat is in the form of a cone with diameter 10.5 m and height 3 m. It is to be covered with canvas to protect it from rain. (i) Find the volume of wheat. (ii) Find the slant height, correct to two decimal places, taking the square root of 36.5625 as 6.05. (iii) Find the area of canvas required. (Take pi = 3.14.) (5 marks)

Read the passage and answer the questions. A football has a radius of 11 cm. Leather costs Rs 0.50 per sq cm. (i) Find the surface area of the football. (ii) Find the cost of leather to cover it. (iii) Find the volume of air in it. (Take pi = 22/7, give the volume to the nearest whole number.) (5 marks)

Read the passage and answer the questions. A school builds a hemispherical dome of radius 7 m over its auditorium. (i) Find the curved surface area of the dome. (ii) Find the cost of painting it at Rs 25 per square m. (iii) Find the volume of air inside the dome, to the nearest cubic m. (Take pi = 22/7.) (5 marks)

Draw a labelled figure and derive the formula for the total surface area of a cone. Use it to find the total surface area of a cone of radius 21 cm and slant height 29 cm. (Take pi = 22/7.) (6 marks)

Draw a figure of a solid made of a cone mounted on a hemisphere, both of radius 7 cm, with the cone's height 24 cm. Find the total surface area and volume of the solid. (Take pi = 22/7.) (6 marks)

A metallic sphere of radius 10.5 cm is melted and recast into small cones, each of radius 3.5 cm and height 3 cm. Draw rough figures and find the number of cones formed. (6 marks)

A conical tent of height 8 m and base radius 6 m is made of canvas 3 m wide. Draw a labelled figure. Find the length of canvas needed, taking pi = 3.14 and allowing an extra 20 cm length for stitching and wastage. (6 marks)

Draw a cone, a hemisphere and a cylinder of the same radius r and height r. Show that their volumes are in the ratio 1 : 2 : 3. (6 marks)